Question #4fa34

1 Answer
Oct 1, 2017

Just Divide x2 by (x-1) Using division Algorithm
we get x2x1=x+1+1x1
1 in last term is remainder
and
(x2x1)dx=(x+1+1x1)dx
=x22+x+log(x1)+c

OR

x2x1dx=x22x+1+2x1x1dx
=(x1)2+2x1x1dx
=((x1)2x1+2x1x1)dx
=((x1)+x+x1x1)dx
=((x1)+1+xx1)dx
=((x1)+1+x+11x1)dx
=((x1)+1+1+1x1)dx
=((x1)+2+1x1)dx
=x22x+2x+log(x1)+c
=x22+x+log(x1)+c